Question

If f(x)=ax^4 - 6x^2 × x+7 and f(-2)=5. what is the value of f(2).
(a) 5
(b) 7
(c) 9
(d) 11​

Answer 1

Question:

If f(x)=ax^4 - 6x^2 × x+7 and f(-2)=5. what is the value of f(2).

(a) 5

(b) 7

(c) 9

(d) 11

Answer:

(c) 9

Answer 2

ANSWER:

Given:

• f(x) = ax^4 - 6x^2 + x + 7
• f(-2) = 5

To Find:

• Value of f(2)

Solution:

$\longrightarrow f(x)=ax^4-6x^2+x+7\\\\\text{We are given that,}\\\\:\implies f(-2)=5\\\\\text{Putting value of x = -2, in f(x),}\\\\:\implies f(-2)=a(-2)^4-6(-2)^2+(-2)+7\\\\:\implies f(-2)=a(16)-6(4)+(-2)+7\\\\:\implies 5=16a-24-2+7\\\\:\implies 5=16a-19\\\\\text{Transposing (-19) to LHS,}\\\\:\implies5+19=16a\\\\:\implies16a=24\\\\\text{Transposing 16 to RHS,}\\\\:\implies a=\dfrac{24\!\!\!\!/^{\:3}}{16\!\!\!\!/_{\:2}}\\\\:\implies a=\dfrac{3}{2}.\\\\\text{So,}\\\\:\implies f(x)=\dfrac{3}{2}x^4-6x^2+x+7\\\\\text{Putting value of x = 2, in f(x),}\\\\:\implies f(2)=\dfrac{3}{2}(2)^4-6(2)^2+(2)+7\\\\:\implies f(2)=\dfrac{3}{2\!\!\!/}16\!\!\!\!/^{\:8}\,-6(4)+2+7\\\\:\implies f(2)=8(3)-24+2+7\\\\:\implies f(2)=24\!\!\!\!/\:-24\!\!\!\!/\:+9\\\\\bf{:\implies f(2)=9}$