Given h(x)= x² and g(x) √(x - 2)= x-2 evaluate: (a) h(g(18)) (b) g(h(4)) (c) (g•g)(11) (d) h(h(0)) (e) (hog)(38) () (g•h)(0)

Question

Given h(x)= x² and g(x)
`√(x - 2)`= x-2 evaluate: (a) h(g(18)) (b) g(h(4)) (c) (g•g)(11) (d) h(h(0)) (e) (hog)(38) () (g•h)(0)

Answer 1

`h(x)=x^2+11`
`g(x)=\sqrt[]{x-2}`
`a)h(g(18))`

first we have to do g(18), then evaluate the number that we get in h

`\sqrt[]{18-2}=\sqrt[]{16}=4`
`x^2+11=4^2+11=16+11=27`

so the a is 27

`b)g(h(4))`
`x^2+11=4^2+11=16+11=27`
`\sqrt[]{27-2}=\sqrt[]{25}=5`

the b is 5

`c)(g\circ g)(11)`
`\sqrt[]{11-2}=\sqrt[]{9}=3`
`\sqrt[]{3-2}=\sqrt[]{1}=1`

the c is 1

`d)h(h(0))`
`x^2+11=0+11=11`
`11^2+11=121+11=132`

the d is 132

`e)(h\circ g)(38)`
`\sqrt[]{38-2}=\sqrt[]{36}=6`
`6^2+11=36+11=47`

the e is 47

`f)(g\circ h)(0)`
`x^2+11=0^2+11=11`
`\sqrt[]{11-2}=\sqrt[]{9}=3`

the f is 3