Question

For the function f(x) = x^ 2+ 5x - 2, find (b) f(-x)(c)-f(x)(d) f(3x) (e) f(x +h)-f(x) /h × h ≠ 0

Answer 1

we have

f(x)=x^2+5x-2

Part a) Find f(3)

For x=3

f(3)=3^2+5(3)-2

f(3)=22

Part b) f(-x)

f(-x)=(-x)^2+5(-x)-2

f(-x)=x^2-5x-2

Part c) -f(x)

-f(x)=-(x^2+5x-2)

so

-f(x)=-x^2-5x+2

Part d) f(3x)

f(3x)=(3x)^2+5(3x)-2

f(3x)=27x^2+15x-2

Part e) {f(x+h)-f(x)}/h

f(x+h)=(x+h)^2+5(x+h)-2

f(x+h)=x^2+2xh+h^2+5x+5h-2

f(x)=x^2+5x-2

Find the difference

{f(x+h)-f(x)}=(x^2+2xh+h^2+5x+5h-2)-x^2-5x+2

{f(x+h)-f(x)}=2xh+h^2+5h

therefore

{f(x+h)-f(x)}/h=2x+h+5