Question

Given f(x)=2x2+3 and g(x) = 5x+2, how do you find 3f(2)−2g(2)f(1)+g(1)?

Answer 1

$\huge{\ulcorner{\red{\bold{Answer}}}}\rfloor$

$\large{\star} \textsf{Given that :- }$

• $f(x) = 2x^2 + 3$

• $g(x) = 5x + 2$

$\large{\star} \textsf{In order to find :- }$

→ $3f(2) - 2g(2) \times f(1) + g(1)$

$\large{\star} \textsf{ We will first find :- }$

(i)

$3 \times f(2)$

$\textbf{ By replacing x = 2}$

$= 3 \times [ 2(2)^2 + 3 ]$

$= 3 \times [ 2(4) + 3 ]$

$= 3 \times [ 8 + 3 ]$

$= 3 \times [11]$

$= 33$

(ii)

$2 \times g(2)$

$\textbf{ By replacing x = 2}$

$= 2 \times [ 5(2) + 2 ]$

$= 2 \times [ 10 + 2 ]$

$= 2 \times [ 12]$

$= 24$

(iii)

$f(1)$

$\textbf{ By replacing x = 1}$

$= 2(1)^2 + 3$

$= 2(1) + 3$

$= 2 + 3$

$= 5$

(iv)

$g(1)$

$\textbf{ By replacing x = 1}$

$= 5(1) + 2$

$= 5 + 2$

$= 7$

$\large{\star} \textsf{ Now replacing values :- }$

$3f(2) - 2g(2) \times f(1) + g(1)$

$= 33 - (24 \times 5) + 7$

$= 33 - 120 + 7$

$= 40 - 120$

$= -80$

$\boxed{\large{\star} \textsf{ So Answer = -80 }}$