Given fx ex gx 2x2 5x 3 and kx x7 Find gfx bfgx gx h g

Given: f(x) = e^x, g(x) = 2x^2 - 5x -3, and k(x) = x^7, Find: g(f(x)) b.(f.g)(x) g(x + h)- g (x)/h f(g(1)) e. the average rate of change of g(x) between x = 0 and x =3. k(x+h) - k(x)/h g. (k o f (x)

Solution

3)g(x)=2x²-5x-3 ,f(x)=e^x

a)g(f(x))=2(e^x)²-5e^x-3

g(f(x))=2e^2x-5e^x-3

b)(f.g)(x)

=f(g(x))

=e^{2x^2-5x-3}

if it is (fxg)(x)

=f(x) x g(x)

=e^x(2x²-5x-3)

c)[g(x+h)-g(x)]/h

=[(2(x+h)²-5(x+h)-3)-(2x²-5x-3)]/h

=[(2x²+4xh+2h²-5x-5h-3)-(2x²-5x-3)]/h

=[4xh+2h²-5h]/h

=4x+2h-5

d)f(g(x))=e^{2x^2-5x-3}

f(g(1))=e^{2*1^2-5*1-3}

f(g(1))=e^-6

e)average rate of change =[g(3)-g(0)]/[3-0]

=[(2*3²-5*3-3)-(2*0²-5*0-3)]/3

=(2*3²-5*3)/3

=(2*3 -5)

=6-5

=1