Question

Find the indicated function given f(x)=2x^2+1 and g(x)=3x-5Answer in simplified answers in descending powers of x.

Answer 1

We will have the following:

1. f(g(2)):

`g(2)=3(2)-5\Rightarrow g(2)=1`

`\Rightarrow f(g(2))=2(1)^2+1\Rightarrow f(g(2))=3`

2. f(g(x)):

`f(g(x))=2(3x-5)^2+1\Rightarrow f(g(x))=2(9x^2-30x+25)+1`

`\Rightarrow f(g(x))=18x^2-60x+51`

3. g(f(x)):

`g(f(x))=_{}3(2x^2+1)-5\Rightarrow g(f(x))=6x^2-2`

4. (g ° g)(x):

`(g\circ g)(x)=3(3x-5)-5\Rightarrow(g\circ g)(x)=9x-20`

5. (f ° f)(x):

`(f\circ f)(x)=2(2x^2+1)^2+1\Rightarrow(f\circ f)(x)=2(4x^4+4x^2+1)+1`

`\Rightarrow(f\circ f)(x)=8x^4+8x^2+3`