Question

Precalculus: Function Algebra Unit 2 Test Part 2

Analyze the work Michael has shown to find the inverse of h(x)=√x −5. Find the error in his work and/or solution and explain what he should have done instead.

Graph both f(x) and its corrected inverse, f-1(x)

Show Work

Answer 1

Explanation:

To find the inverse of the function h(x) = √x - 5, Michael's work needs to be analyzed. However, you didn't provide the work Michael has shown.

Nevertheless, I can explain the correct method to find the inverse of h(x).

To find the inverse of a function, we typically switch the x and y variables and solve for y. In this case, we have the function h(x) = √x - 5.

Step 1: Replace h(x) with y:

y = √x - 5

Step 2: Swap x and y:

x = √y - 5

Step 3: Solve for y:

x + 5 = √y

Step 4: Square both sides of the equation to isolate y:

(x + 5)^2 = (√y)^2

(x + 5)^2 = y

Therefore, the inverse function is:

f^(-1)(x) = (x + 5)^2

To graph both f(x) and its corrected inverse f^(-1)(x), you can plot the original function f(x) = √x - 5 and its inverse f^(-1)(x) = (x + 5)^2 on a coordinate plane.

Please provide Michael's work or let me know if there is anything specific you would like me to explain or analyze.