Question

How do I solve these?If f(x)=3xsquared + 9x-4 then evaluate the following:f(1)=3x^2+9x-4f(x+h)=3x^2+9x-4

Answer 1

`\begin{gathered} a)\text{ }f(1)\text{ = 8} \\ b)\text{ }f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}`

Step-by-step explanation:
`\begin{gathered} The\text{ given function:} \\ f(x)=3x^2\text{ + 9x - 4} \end{gathered}`

a) We need to evaluate when x = 1

f(1): this means we will replace x with 1 in the given function

`\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f\mleft(1\mright)=3(1)^2+9(1)-4 \\ f(1)\text{ = 3(1) + 9 - 4 = 3 + 9 - 4} \\ f(1)\text{ = 8} \end{gathered}`

b) We need to evaluate the function when x = x + h

`\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f(x\text{ + h): we will replace x with x + h in the given function} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}`

Expanding:

`\begin{gathered} f(x\text{ + h) }=3(x^2+2xh+h^2)\text{ + 9(x + h) - 4} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \text{Since there are no like terms we can simplify, we can leave it in expanded form:} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \\ or\text{ the non expanded form:} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}`