Question

let f(x) = 3x+2 and g(x) = x^2+x+1 Evaluate the following :

Answer 1

In order to find each of those values, we need to replace x in the appropriate function with the entry given for that function.

Part a

Replace x with 3 in the expression 3x+2:

$f(3)=3\cdot3+2=9+2=11$

Part b

Replace x with -2 in the expression 3x+2:

$f(-2)=3\cdot(-2)+2=-6+2=-4$

Part c

Replace x with -1 in the expression x²+x+1:

$g(-1)=(-1)^{2}+(-1)+1=1-1+1=1$

Part d

Replace x with 3 in the expression x²+x+1:

$g(3)=3^{2}+3+1=9+4=13$

Part e

Replace x with a-2 in the expression 3x+2:

$f(a-2)=3\cdot(a-2)+2=3a-6+2=3a-4$

Part f

Replace x with a-2 in the expression x²+x+1:

$\begin{gathered} g(a-2)=\mleft(a-2\mright)^2+\mleft(a-2\mright)+1 \\ \\ =a^{2}-4a+4+a-2+1 \\ \\ =a^{2}-3a+3 \end{gathered}$