Question

Let f(x) = 2x^2+ 3x – 1. Evaluate the following expressions.f(2x) + f(3x)

Answer 1

Recall that to evaluate a given function we substitute the given value wherever x appears, then:

`\begin{gathered} f(2x)=2(2x)^2+3(2x)-1, \\ f(3x)=2(3x)^2+3(3x)-1. \end{gathered}`

Substituting the above equations in the given expression we get:

`f\mleft(2x\mright)+f\mleft(3x\mright)=2(2x)^2+3(2x)-1+2(3x)^2+3(3x)-1.`

Simplifying the above equation we get:

`\begin{gathered} f\mleft(2x\mright)+f\mleft(3x\mright)=2\mleft(4x^2\mright)^{}+3\mleft(2x\mright)-1+2\mleft(9x^2\mright)^{}+3\mleft(3x\mright)-1, \\ f\mleft(2x\mright)+f\mleft(3x\mright)=8x^2+6x-1+18x^2+9x-1. \\ f\mleft(2x\mright)+f\mleft(3x\mright)=26x^2+15x-2. \end{gathered}`

Answer:

`f(2x)+f(3x)=26x^2+15x-2.`