You visited us 1 times! Enjoying our articles? Unlock Full Access!

Division Algorithm for a Polynomial

If fx = 3x ...

Question

If $f (x) = 3 x - 5$ and $g (x) = x^{2} + 1, f [g (x)] =$

3 x^{2} - 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 x^{2} + 6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} - 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 x^{2} - 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 x^{2} + 5 x - 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $3 x^{2} - 2$
Given $f (x) = 3 x - 5$ and $g (x) = x^{2} + 1$
$∴ f (g (x)) = f (x^{2} + 1)$
$= 3 (x^{2} + 1) - 5$
$= 3 x^{2} - 2$

Suggest Corrections

Similar questions

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

(i)

(ii)

(iii)

f (x) = 3 x^{2} - 5

g (x) = \frac{x}{x^{2} + 1}

(g o f) (x)

f (x) = c o t^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}}), g (x) = c o s^{- 1} (\frac{1 - x^{2}}{1 + x^{2}})

f (x) = g (x)

x = \frac{\sqrt{25 - 10 \sqrt{5}}}{5}

s i n 18^{o} = \frac{\sqrt{5} - 1}{4}

f (x) = x^{3} - 3 x^{2} + 5 x - 3

x^{2}

f (x) = 3 x^{2} - 5 x - 1

(f \circ g) (x) = 3 x^{2} + 7 x + 1,

INCORRECT ?

Join BYJU'S Learning Program