Question 85188
a.
{{{f(x)=3x^5-5x^3+2x^2+6}}} Start with the given equation

{{{f(0)=3(0)^5+-5(0)^3+2(0)^2+6}}} Plug in x=0

{{{f(0)=3(0)+-5(0)+2(0)+6}}} Raise 0 to the respective exponent values

{{{f(0)=0+0+0+6}}} Multiply

{{{f(0)=6}}} Add


b.

{{{f(x)=3x^5-5x^3+2x^2+6}}} Start with the given equation

{{{f(2)=3(2)^5+-5(2)^3+2(2)^2+6}}} Plug in x=2

{{{f(2)=3(32)+-5(8)+2(4)+6}}} Raise 2 to the respective exponent values

{{{f(2)=96+-40+8+6}}} Multiply

{{{f(2)=70}}} Add


c.
{{{f(x)=3x^5-5x^3+2x^2+6}}} Start with the given equation

{{{f(-2)=3(-2)^5+-5(-2)^3+2(-2)^2+6}}} Plug in x=-2

{{{f(-2)=3(-32)+-5(-8)+2(4)+6}}} Raise -2 to the respective exponent values

{{{f(-2)=-96+40+8+6}}} Multiply

{{{f(-2)=-42}}} Add

d.

{{{f(x)=3x^5-5x^3+2x^2+6}}} Start with the given equation

{{{f(2x)=3(2x)^5+-5(2x)^3+2(2x)^2+6}}} Plug in x=2x

{{{f(2x)=3(32x^5)+-5(8x^3)+2(4x^2)+6}}} Raise 2x to the respective exponent values

{{{f(2x)=96x^5-40x^3+8x^2+6}}} Multiply