f(x)=2x+5, g(x)=x^2-3 and h(x)=7-x/3

Question

Compute (f-h)(4)

Evaluate the following compositions: (f o g)(x) and (h o g)(x)

Find the inverse functions: f^-1(x) and h^-1(x)

Answer 1

Given functions f(x) = 2x+5, g(x) = x^2-3 and h(x) = 7-x/3

1)(f-h)(4) = (f(x)-h(x))(4)

f(x)-h(x)= 2x+5-(7-x/3)

= 2x+5-7+x/3

= 2x-2+x/3

(f-h)(4) = 2(4)-2+4/3

= 8-2+4/3

= 6+4/3

= 22/3

2) fog(x) = f(g(x))

= f(x^2-3)

= 2(x^2-3)+5

= 2x^2-6+5

= 2x^2-1

3) hog)(x) = h(g(x))

= h(x^2-3)

= 7-(x^2-3)/3

= (21-x^2+3)/3

= (-x^2+24)/3

=-x^2/3+8

Answer 2

4) f(x) = 2x+5

f(x) = y

f^-1f(x) = f^-1(y) = x

y = 2x+5

Subtrct 5 from eachside.

y-5 = 2x+5-5

y-5 = 2x

Divide to each side by 2.

(y-5)/2 = 2x/2

(y-5)/2 = x

x = (y-5)/2

5) Now h^-1(x)

h(x) = 7-x/3

y = 7-x/3

Subtract 7 from each side.

y-7 = 7-7-x/3

y-7 = -x/3

Multiple to each side by negitive 3.

-3(y-7) = -(-3)x/3

-3y+21 = x

x = -3y+21