Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x³ to find (g^-1 _º f^-1) (-5) .

Question

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x³ to find (g^-1 _º f^-1)(-5). A)-2 B)0 C)-4 D)2 E)4

Quizplus · Accepted Answer

First, find $ f^{-1}(x) $: If $ y = \frac{1}{8}x - 5 $, then $ x = \frac{1}{8}y - 5 $. Solving for $ y $, we get $ y = 8(x + 5) $. Thus, $ f^{-1}(x) = 8(x + 5) $.  Next, find $ g^{-1}(x) $: If $ y = x^3 $, then $ x = y^{1/3} $. Thus, $ g^{-1}(x) = x^{1/3} $.  Now, compute $ (g^{-1} \circ f^{-1})(-5) $:  $ f^{-1}(-5) = 8(-5 + 5) = 8(0) = 0 $.  Then, $ g^{-1}(0) = 0^{1/3} = 0 $.  Therefore, the answer is 0.

Use the Functions Given By f(x)=18x−5f ( x ) = \frac { 1 } { 8 } x - 5f(x)=81​x−5

Use the Functions Given By $f ( x ) = \frac { 1 } { 8 } x - 5$