Question

Let f(x) = -4x + 7 and g(x) = 10x - 6, find f(g(x)).

-40x + 24

-40x + 31

-40x + 64

-40x + 70

Answer 1

@jim_thompson5910 @Mertsj @jdoe0001 @whpalmer4 @tkhunny @Preetha @Jamierox4ev3r @studyislandhelp @Awesome781

Answer 2

f(x) = -4x + 7


f(g(x)) = -4(g(x)) + 7 ... replace EVERY x with g(x)


f(g(x)) = -4(10x - 6) + 7 ... replace g(x) on the right side with 10x - 6


I'll let you finish up.

Answer 3

\(\bf f(x) = -4x + 7 \qquad g(x) = {\color{red}{ 10x - 6}}
\\ \quad \\
f(\quad g(x)\quad )=-4({\color{red}{ \square ? }}) + 7\)

Answer 4

@jdoe0001 can you help me and elaborate on this?

Answer 5

hmmm not much to elaborate really

g(x) <-- the whole function, TAKES OVER any "x" in f(x)

that's what f( g(x) ) means

Answer 6

i dont understand how to work it out can you help me step by step

Answer 7

\(\bf \bf f(x) = -4x + 7 \qquad g(x) = {\color{red}{ 10x - 6}}
\\ \quad \\
f(\quad g(x)\quad )=-4({\color{red}{ 10x - 6}}) + 7\) <-- see it now?

Answer 8

so it would be -40x+24

Answer 9

yes, don't forget the +7 at the end

Answer 10

\(\bf f(x) = -4x + 7 \qquad g(x) = {\color{red}{ 10x - 6}}
\\ \quad \\
f(\quad g(x)\quad )=-4({\color{red}{ 10x - 6}}) + 7\implies -40x+24+7\implies -40x+31\)

Answer 11

@jdoe0001 so the answer is b?

Answer 12

yeap

Answer 13

can i ask you one more question @jdoe0001

Answer 14

ok

Answer 15

Let f(x) = x2 - 16. Find f-1(x).

4square root of x

±square root of x plus 16

x squared over 16

1 over quantity of x squared minus 16

Answer 16

to find the "inverse relation"
what we simply do is, swap about the variables and then solve for "y", so \(\bf f(x) = {\color{red}{ y}}={\color{blue}{ x}}^2 - 16\implies {\color{blue}{ x}}={\color{red}{ y}}^2 - 16\)

and then you'd solve it for "y"

Answer 17

would it be c? if not then its d

Answer 18

\(\bf f(x) = {\color{red}{ y}}={\color{blue}{ x}}^2 - 16\implies {\color{blue}{ x}}={\color{red}{ y}}^2 - 16
\\ \quad \\
\textit{adding 16 to both sides }\implies x+16=y^2
\\ \quad \\
\textit{taking }\sqrt{\qquad }\textit{ to both sides}\implies \sqrt{x+16}=\sqrt{y^2}
\\ \quad \\
\implies \sqrt{x+16}=y=f^{-1}(x)\)

Answer 19

so its b?

Answer 20

yeap

Answer 21

thanks so much @jdoe0001 :)

Answer 22

yw