find the inverse of each of the given functions.

$f(x) = 4x - 12$

$f^{-1}(x) = \square x + \square$

$h(x) = \frac{2x - 4}{3}$

$h^{-1}(x) = \frac{3x - 12}{2}$
$h^{-1}(x) = \frac{3}{(2x - 4)}$
$h^{-1}(x) = \frac{3x + 4}{2}$

Question

find the inverse of each of the given functions.

$f(x) = 4x - 12$

$f^{-1}(x) = \square x + \square$

$h(x) = \frac{2x - 4}{3}$

$h^{-1}(x) = \frac{3x - 12}{2}$
$h^{-1}(x) = \frac{3}{(2x - 4)}$
$h^{-1}(x) = \frac{3x + 4}{2}$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Inverse Functions", "Finding Inverses Algebraically" ], "current_concepts": [ "Inverse Functions", "Finding Inverses Algebraically" ] } ## Find the inverse of $f(x)$ $$ \begin{aligned} y &= 4x - 12 \ x &= 4y - 12 \ 4y &= x + 12 \ y &= \frac{1}{4}x + 3 \ f^{-1}(x) &= \frac{1}{4}x + 3 \end{aligned} $$ ## Find the inverse of $h(x)$ $$ \begin{aligned} y &= \frac{2x - 4}{3} \ x &= \frac{2y - 4}{3} \ 3x &= 2y - 4 \ 2y &= 3x + 4 \ y &= \frac{3x + 4}{2} \ h^{-1}(x) &= \frac{3x + 4}{2} \end{aligned} $$ ## Question 1 $f^{-1}(x) =$ $\frac{1}{4}$ $x +$ $3$ ## Question 2 (A) $h^{-1}(x) = \frac{3x - 12}{2}$

(B) $h^{-1}(x) = \frac{3}{(2x - 4)}$

(C) $h^{-1}(x) = \frac{3x + 4}{2}$

{ "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Functions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the inverse of \(f(x)\)

Find the inverse of \(h(x)\)

Answer:

Question 1

Question 2