Question

If(x)= x² + 2, and g(x)=5x-8 then find (i)(f+g) (1) (ii) (f.g)​

Answer 1

Step-by-step explanation:

This is tge required answer

Answer 2

We need to recall the following rules of a function.

• $(f+g)(x)=f(x)+g(x)$
• $(f\cdot g)(x)=f(x)\cdot g(x)$

Given:

$f(x)=x^2+2$

$g(x)=5x-8$

i) $(f+g)(1)$

$(f+g)(x)=x^{2} +2+5x-8$

$(f+g)(x)=x^{2} +5x-6$

substitute $x=1$, we get

$(f+g)(1)=1^{2} +5(1)-6$

$(f+g)(1)=6-6$

$(f+g)(1)=0$

ii)  $(f\cdot g)(1)$

$(f\cdot g)(x)=(x^{2} +2)(5x-8)$

$(f\cdot g)(x)=5x^{3} -8x^2+10x-16$

substitute $x=1$, we get

$(f\cdot g)(1)=5(1)^{3} -8(1)^2+10(1)-16$

$(f\cdot g)(1)=5 -8+10-16$

$(f\cdot g)(1)=-9$