F x - x -1 and g x - x 2-2 - Find gof -1-2-1-A- 0-2B- -0-1-C- -2-0-D- none of these

The correct option is C [ 2, 0]Option (d) gof (x) = g(f(x))= g(x+1) = (x+1)2 2= x2 +2x 1 2 ≤x2 +2x 1≤ 1 1≤x2 +2x≤0 x(x+2) ≤0 2 ≤ x ≤ 0 [ 2,0] ...

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

Byju's Answer

Other

Quantitative Aptitude

Functions

f x = x +1 an...

Question

f(x)= x+1 and g(x)= x² -2. Find(gof)^-1([-2,-1])

(0,-2)

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

[0,-1]

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

[-2, 0]

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

none of these

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

Open in App

Solution

The correct option is C [-2, 0]
Option (d)

gof (x) = g(f(x))= g(x+1) = (x+1)²-2= x² +2x -1

-2 ≤x² +2x -1≤-1

-1≤x² +2x≤0

x(x+2) ≤0

- 2 ≤ x ≤ 0

[-2,0]

Suggest Corrections

Similar questions

Q. f(x) = x+1 and g(x) =

x^{2} - 2

. Find (gof) at x = 2?

Q. Let

f (x) = x^{2} + 2 b x + 2 c^{2}

and

g (x) = - x^{2} - 2 c x + b^{2}, b, c \neq 0

. If the minimum of

f (x)

is greater than maximum value of

g (x)

, then the range of

\frac{b}{c}

Q. Let

f (x) = e^{x} - x

and

g (x) = x^{2} - x, \forall x \in R

. Then the set of all

x \in R

, where the function

h (x) = (f \circ g) (x)

is increasing, is :

Q. Find fog and gof if
(i)

f (x) = e^{x}, g (x) = \log_{e} x

(ii)

f (x) = x^{2}, g (x) = \cos x

(iii)

f (x) = | x |, g (x) = \sin x

(iv)

f (x) = x + 1, g (x) = e^{x}

(v)

f (x) = \sin^{- 1} x, g (x) = x^{2}

(vi)

f (x) = x + 1, g (x) = \sin x

(vii)

f (x) = x + 1, g (x) = 2 x + 3

(viii)

f (x) = c, c \in R, g (x) = \sin x^{2}

(ix)

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

Q. Let

f (x) = x^{2} and g (x) = 2^{x}

. Then, the solution set of the equation

f o g (x) = g o f (x)

is
(a) R
(b) {0}
(c) {0, 2}
(d) none of these

Join BYJU'S Learning Program

f(x)= x+1 and g(x)= x2 -2. Find(gof)-1([-2,-1])

The correct option is C [-2, 0]Option (d) gof (x) = g(f(x))= g(x+1) = (x+1)2-2= x2 +2x -1 -2 ≤x2 +2x -1≤-1 -1≤x2 +2x≤0 x(x+2) ≤0 - 2 ≤ x ≤ 0 [-2,0]

f(x)= x+1 and g(x)= x² -2. Find(gof)^-1([-2,-1])

The correct option is C [-2, 0]
Option (d)

gof (x) = g(f(x))= g(x+1) = (x+1)²-2= x² +2x -1

-2 ≤x² +2x -1≤-1

-1≤x² +2x≤0

x(x+2) ≤0

- 2 ≤ x ≤ 0

[-2,0]