Trying to find the right answer to this..

f : R → R such that f (x) = cos x and g : R → R such that g (a ) = 3 x 2 . Now (g o f) (x) = g (f(x)) = g (cos x) = 3 cos 2 x and (f o g)) (x) = f (g (x)) = f(3 x 2 ) = cos (3 x 2 ) Now 3 cos 2 x ≠ cos (3x 2 ) ∴ g o f ≠ f o g.

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Relations and Functions

Short Answer Type

261.

Find the number of all one-one functions from set A = {1, 2, 3} to itself.

131 Views

262. Let f : X → Y be a function. Define a relation R in X given by R = {(a, b) : f (q) = f(b)}. Examine if R is an equivalence relation.

150 Views

263.

Let f : Z → Z, g : Z → Z be functions defined by
f = {(n, n²): n ∈ Z} and g = {(n | n |²): n ∈ Z}. Show that f = g.

131 Views

264.

Let f : R → R be defined as f (x) = x⁴ Choose the correct answer.

(A) f is one-one onto (B) f is many-one onto
(C) f is one-one but not onto (D)f is neither one-one nor onto.

134 Views

265.

Let f : R → R be defined as f (x) = 3 x. Choose the correct answer. (A) f is one-one onto (B) f is many-one onto
(C) f is one-one but not onto (D) f is neither onc-one nor onto.

129 Views

266. Let f : {2, 3, 4, 5} → {3, 4, 5, 9 } and g : {3, 4, 5,9} → {7, 11, 15} be functions defined as f (2) = 3, f (3) = 4, f(4) = f(5) = 5 and g (3) = g (4) = 7 and g (5) = g (9) = 11. Find g of.

478 Views

267. Let f : {11, 3, 4} → {1, 2, 5} and g : {1, 2. 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down go f.

168 Views

268. Find g o f and f o g, if f : R → R and g : R → R are given by f (x) = cos x and g (x) = 3 x^-2. Show that g o f ≠ f o g.

f : R → R such that f (x) = cos x and g : R → R such that g (a ) = 3 x².
Now (g o f) (x) = g (f(x)) = g (cos x) = 3 cos² x and (f o g)) (x) = f (g (x)) = f(3 x²) = cos (3 x²)
Now 3 cos² x ≠ cos (3x²) ∴ g o f ≠ f o g.

237 Views