Question

Find f(g(x)).
f(x)= sqrt of x+3 g(x) = 8x - 7

Answer 1

@jim_thompson5910

Answer 2

is f(x) the function \[\Large f(x) = \sqrt{x}+3\]

or is it \[\Large f(x) = \sqrt{x+3}\]

Answer 3

2nd one

Answer 4

first replace every x with g(x)

\[\Large f(x) = \sqrt{x+3}\]

\[\Large f(g(x)) = \sqrt{g(x)+3}\]

Answer 5

then on the right side, replace g(x) with 8x-7 (since g(x) = 8x-7) and simplify

Answer 6

so our full step by step work looks like this

\[\Large f(x) = \sqrt{x+3}\]

\[\Large f(g(x)) = \sqrt{g(x)+3}\]

\[\Large f(g(x)) = \sqrt{8x-7+3}\]

\[\Large f(g(x)) = \sqrt{8x-4}\]

Answer 7

I guess you could pull out a 4 and simplify, but I think this is far enough for the teacher to be satisfied

Answer 8

I think it is supposed to be simplified
So if i simplify it, it would be 2 sqrt of 2x-1?

Answer 9

Good,

\[\Large f(g(x)) = \sqrt{8x-4}\]

\[\Large f(g(x)) = \sqrt{4(2x-1)}\]

\[\Large f(g(x)) = \sqrt{4}*\sqrt{2x-1}\]

\[\Large f(g(x)) = 2\sqrt{2x-1}\]

Answer 10

Thank you!! I understand it now

Answer 11

I'm glad you do

Answer 12

Can you help me with one more problem i'm stuck on?

Answer 13

sure