Question

Find functions f and g so that h(x) = (f ∘ g)(x).
h(x) = (6x - 14)8
A. f(x) = 6x - 14, g(x) = x8
B. f(x) = 6x8 - 14, g(x) = -14
C. f(x) = x8, g(x) = 6x - 14
D. f(x) = (6x)8, g(x) = -14

Answer 1

so got any suspects in mind?

Answer 2

care to try any of the choices? which one do you think we could try?

Answer 3

Tbh I have no idea how to do this, but I would love to learn how to!

Answer 4

ok... gimme a choice to try to see if it works

Answer 5

B. f(x) = 6x8 - 14, g(x) = -14

Answer 6

B, ok let's see if B works
\(\bf h(x) = (6x - 14)^8
\\ \quad \\ \quad \\
(B) \qquad f(x) = 6x^8 - 14\qquad {\color{red}{ g(x)}} = -14
\\ \quad \\
(f \ o \ g)(x)\implies f(\quad g(x)\quad )=6({\color{red}{ g(x)}})^8 - 14\implies 6({\color{red}{ -14}})^8
\\ \quad \\ \quad \\
6({\color{red}{ -14}})^8 - 14 \ne (6x - 14)^8\)


so no dice on that one

what about another choice?

Answer 7

D. f(x) = (6x)8, g(x) = -14

Answer 8

\(\bf h(x) = (6x - 14)^8
\\ \quad \\ \quad \\
(D) \qquad f(x) = (6x)^8 - 14\qquad {\color{red}{ g(x)}} = -14
\\ \quad \\
(f \ o \ g)(x)\implies f(\quad g(x)\quad )=[6({\color{red}{ -14}})]^8 - 14
\\ \quad \\

[6({\color{red}{ -14}})]^8 - 14 \ne (6x - 14)^8\)

no dice on that one either
what about another one?

Answer 9

hmm actaully it has no 14.. lemme fix that

Answer 10

\((\bf h(x) = (6x - 14)^8
\\ \quad \\ \quad \\
(D) \qquad f(x) = (6x)^8 \qquad {\color{red}{ g(x)}} = -14
\\ \quad \\
(f \ o \ g)(x)\implies f(\quad g(x)\quad )=[6({\color{red}{ -14}})]^8
\\ \quad \\

[6({\color{red}{ -14}})]^8 \ne (6x - 14)^8\)

so... no dice anyhow
another choice?

Answer 11

Is choice (B) transcribed correctly?

Answer 12

yes, keep in mind that g(x) is just a constant

Answer 13

C. f(x) = x8, g(x) = 6x - 14

Answer 14

no, choice (B)

Answer 15

C, let's try that one then \(\bf f(x) = x8, g(x) = 6x - 14 \\
h(x) = (6x - 14)^8
\\ \quad \\ \quad \\
(D) \qquad f(x) = x^8 \qquad {\color{red}{ g(x)}} = 6x -14
\\ \quad \\
(f \ o \ g)(x)\implies f(\quad g(x)\quad )=({\color{red}{ 6x -14}})^8
\\ \quad \\

({\color{red}{ 6x -14}})^8 \iff (6x - 14)^8\)

Answer 16

got the wrong letter choice anyhow \(\bf h(x) = (6x - 14)^8
\\ \quad \\ \quad \\
(C) \qquad f(x) = x^8 \qquad {\color{red}{ g(x)}} = 6x -14
\\ \quad \\
(f \ o \ g)(x)\implies f(\quad g(x)\quad )=({\color{red}{ 6x -14}})^8
\\ \quad \\

({\color{red}{ 6x -14}})^8 \iff (6x - 14)^8\)

Answer 17

So C is correct?

Answer 18

f ( g(x) ) <---- as you can see, means, g(x) will replace any "x" in the function f(x)

so yes, it's C

Answer 19

Gotcha! (: Thank you very much

Answer 20

yw