Question

If $f(x-1)=3x^2+5x+6$, find the value of f(x + 1).

• A. 3x² + 17x + 28
• B. 3x² + 17x – 28
• C. 3x² + 16x + 25
• D. 3x² - 16x + 25

Answer 1

The correct option is A 3x² + 17x + 28

f(x-1) = $3x^2+5x+6$

Put x = x + 2, f(x + 2 – 1) = $3(x+2{)}^2$ + 5(x+2) + 6

f( x + 1)= 3($x^2$ + 4 + 4x) + 5x + 16

= $3x^2$ + 12 + 12x + 5x + 16

= $3x^2$ + 17x + 28

Hence option (a)

Shortcut
a) Assumption method

Assume x = 1

f(0) = 14, f(2) = 48

Among the answer options, Sub x=1 and check where you are getting 48,

This is obtained only at option (a)

b)

Put x=1 in the question and x=-1 in the option, both should give 14