Question

Hello, will you please tell me how to solve step by step? This is evaluating functions from an equation. We have: f(x)=x2 + 3 (that is x squared) g(x)=x + 1 h(x)=2How do I solve these? 1. f(g(2))=2. g(f)(0))=3. f(g(h(1)))=4. f(y)=5. g(w)=6. h(z)=

Answer 1

`\begin{gathered} f(x)=x^2+3 \\ g(x)=x+1 \\ h(x)=2 \end{gathered}`

1. f(g(2))

Find g(2); evaluate g for x=2

`\begin{gathered} g(2)=2+1 \\ g(2)=3 \end{gathered}`

Find f(g(2)) or f(3)

`\begin{gathered} f(g(2))=f(3)=3^2+3 \\ f(g(2))=9+3 \\ f(g(2))=12 \end{gathered}`

2. g(f(0))

Find f(0)

`\begin{gathered} f(0)=0^2+3 \\ f(0)=3 \end{gathered}`

Find g(f(0)) or g(3)

`\begin{gathered} g(f(0))=g(3)=3+1 \\ g(f(0))=4 \end{gathered}`

3. f(g(h(1)))

Find h(1): (All the values of h are euqual to 2

`h(1)=2`

Find g(h(1)) or g(2):

`g(2)=3`

Find f(g(h(1))) or f(3):

`\begin{gathered} f(g(h(1)))=f(3) \\ f(g(h(1)))=12 \end{gathered}`

4. f(y); substitute the x in f by y:

`f(y)=y^2+3`

5. g(w); substitute the x in g by w:

`g(w)=w+1`

6. h(z); substitute the x in h by z:

`h(z)=2`