Question

What is the inverse of the function f(x) = one-quarterx – 12? h(x) = 48x – 4 h(x) = 48x + 4 h(x) = 4x – 48 h(x) = 4x + 48

Answer 1

h(x) = 4x + 48 ⇒ (D)

Explanation:

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Answer 2

The inverse of the function f(x) is h(x) = 4x + 48 ⇒ (D)

Explanation:

To find the inverse of a function do these steps

1. Replace f(x) by y
2. Switch x and y
3. Solve to find the new y
4. Replace y by
   `f^(-1)`(x)

Let us do these steps to solve the equation

∵ f(x) =
`(1)/(4)`x - 12

→ Replace f(x) by y

∴ y =
`(1)/(4)`x - 12

→ Switch x and y

∴ x =
`(1)/(4)`y - 12

→ Add 12 to both sides

∵ x + 12 =
`(1)/(4)`y - 12 + 12

∴ x + 12 =
`(1)/(4)`y

→ Multiply each term by 4

∵ 4(x) + 4(12) = 4(
`(1)/(4)`y)

∴ 4x + 48 = y

→ Switch the two sides

∴ y = 4x + 48

→ Replace y by h(x)

∴ h(x) = 4x + 48

∴ The inverse of the function f(x) is h(x) = 4x + 48