aglebra 2 help?

Question

If you can just walk me through the steps for each problem, I'd really appreciate it... Thank you so much in advance !!

f(x) = x+1

g(x) = 2x^2 +5

h(x) = 3x-1

1. Find f(g(x))?

2. Find h(f(g(x))?

3. Find g(h(f(x))?

Answer 1

When you have stuff like f(g(x)) and h(f(g(x)) you put the inside equation in place of x.

1. f(g(x))=g(x)+1
you put in g(x) to get the answer: f(g(x))=(2x^2+5)+1
simplify that and f(g(x))=2x^2+6

2. h(f(g(x))=3(f(g(x))-1
put in f(g(x)): h(f(g(x))=3(2x^2+6)-1
Simplify: h(f(g(x))=6x^2+17

3. g(h(f(x))=2(h(f(x)))^2+5=
2(3(x+1)-1)^2+5=
2(3x+2)^2+5=18x^2+12x+13
g(h(f(x))=18x^2+12x+13

Answer 2

Given:

f(x) = x + 1
g(x) = 2x² + 5
h(x) = 3x - 1

Work the problems from the inside out.

1. f(g(x)) = f(2x² +5) = (2x² +5) + 1 = 2x² +6

2. h(f(g(x))) = h(f(2x² +5)) = h{(2x² + 5) + 1} = h(2x² + 6)
= 3(2x² + 6) - 1 = 6x² + 18 - 1 = 6x² + 17

3. g(h(f(x))) = g(h(x + 1)) = g{3(x + 1) - 1} = g(3x + 3 - 1)
= g(3x + 2) = 2(3x + 2)² + 5 = 2(9x² + 12x + 4) + 5
= 18x² + 24x + 8 + 5 = 18x² + 24x + 13

Answer 3

You should put the given function instead of x
f(g(x)) = 2x^2+5 +1 = 2x^2 +6

h(f(g(x)) = 3*(2x^2+6) - 1 =6x^2 +17

h(f(x))= 3(x+1)+1 = 3x+4
g(h(f(x)) = 2*(3x+4)^2 +5 =18x^2+48x+37