which function is the inverse of $f(x) = -5x - 4$?

$f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5}$

$f^{-1}(x) = -\frac{1}{5}x + \frac{4}{5}$

$f^{-1}(x) = -4x + 5$

$f^{-1}(x) = 4x + 4$

Question

which function is the inverse of $f(x) = -5x - 4$?

$f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5}$

$f^{-1}(x) = -\frac{1}{5}x + \frac{4}{5}$

$f^{-1}(x) = -4x + 5$

$f^{-1}(x) = 4x + 4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Finding Inverses Algebraically" ], "new_concepts": [], "current_concepts": [ "Inverse Functions", "Finding Inverses Algebraically" ] } ## Swap variables to find the inverse relation $$ x = -5y - 4 $$ ## Solve for y $$ \begin{aligned} x + 4 &= -5y \ y &= -\frac{1}{5}x - \frac{4}{5} \end{aligned} $$ ## Express in inverse function notation $$ f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5} $$

(A) $f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5}$

(B) $f^{-1}(x) = -\frac{1}{5}x + \frac{4}{5}$

(C) $f^{-1}(x) = -4x + 5$

(D) $f^{-1}(x) = 4x + 4$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Finding Inverses Algebraically" ] }

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QUESTION IMAGE

Question

Explanation:

Swap variables to find the inverse relation

Solve for y

Express in inverse function notation

Answer: