Replace <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> with <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Interchange the variables.

Rewrite the equation as <math><mstyle displaystyle="true"><mn>5</mn><mi>sin</mi><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>7</mn><mo>)</mo></mrow><mo>=</mo><mi>x</mi></mstyle></math> .

Divide each term by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>5</mn><mi>sin</mi><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>7</mn><mo>)</mo></mrow><mo>=</mo><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>7</mn><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Take the inverse sine of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> from inside the sine.

Add <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> to both sides of the equation.

Replace the <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> with <math><mstyle displaystyle="true"><msup><mrow><mi>f</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> to show the final answer.

Set up the composite result function.

Evaluate <math><mstyle displaystyle="true"><mi>g</mi><mrow><mo>(</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> by substituting in the value of <math><mstyle displaystyle="true"><mi>f</mi></mstyle></math> into <math><mstyle displaystyle="true"><mi>g</mi></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>7</mn><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Since <math><mstyle displaystyle="true"><mi>g</mi><mrow><mo>(</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mi>x</mi></mstyle></math> , <math><mstyle displaystyle="true"><msup><mrow><mi>f</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>arcsin</mi><mrow><mo>(</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>)</mo></mrow><mo>+</mo><mn>7</mn></mstyle></math> is the inverse of <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>5</mn><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>7</mn><mo>)</mo></mrow></mstyle></math> .

Do you know how to Find the Inverse f(x)=5sin(x-7)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | one billion four hundred ninety-seven million nine hundred forty-three thousand four hundred fifty-six |
---|

- 1497943456 has 64 divisors, whose sum is
**11375008362** - The reverse of 1497943456 is
**6543497941** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 52
- Digital Root 7

Name | five hundred sixty-two million six hundred fifty-two thousand five hundred ninety-six |
---|

- 562652596 has 32 divisors, whose sum is
**1384799328** - The reverse of 562652596 is
**695256265** - Previous prime number is
**373**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 46
- Digital Root 1

Name | six hundred ninety-four million four hundred three thousand four hundred eleven |
---|

- 694403411 has 4 divisors, whose sum is
**747819072** - The reverse of 694403411 is
**114304496** - Previous prime number is
**13**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 32
- Digital Root 5