Question

PLEASE HELP ASAP PLEASE THANKS

Answer 1

(a) (g·h)(x) = x³√(5x-1)

(b) (g◦h)(x) = √(5x³ -1)

(c) (f+h)(1) = -1/3

(d) (g◦f)(x) = 1.5

Explanation:

As with all function evaluations, put the argument where the variable is, and simplify. The product of functions is the product of their values. The sum of functions is the sum of their values.

Function composition is a function of a function value. The composition is evaluated right to left. That is, (g∘f)(x) = g(f(x)).

(a)

`(g\cdot h)(x)=(√(5x-1))(x^2)\\\\\boxed{(g\cdot h)(x)=x^2√(5x-1)}`

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(b)

`(g\circ h)(x)=g(h(x))=g(x^3)=√(5x^3-1)\\\\\boxed{(g\circ h)(x)=√(5x^3-1)}`

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(c)

`(f+h)(1)=f(1)+h(1)=(1-5)/(1+2)+1^3=-(4)/(3)+1\\\\\boxed{(f+h)(1)=-(1)/(3)}`

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(d)

`(g\circ f)(18)=g(f(18))=g\left((18-5)/(18+2)\right)=g\left((13)/(20)\right)=g(0.65)\\\\=√(5(0.65)-1)=√(2.25)=1.5\\\\\boxed{(g\circ f)(18)=1.5}`