If f:R to R is the function defined by f...

If `f:R to R` is the function defined by `f(x)=4x^(3) +7`, then show that f is a bijection.

Topper's Solved these Questions

QUESTION PAPER 2020
SHARAM PUBLICATION|Exercise EXERCISE|47 Videos
THREE DIMENSIONAL GEOMETRY
SHARAM PUBLICATION|Exercise EXAMPLE|96 Videos

Similar Questions

Explore conceptually related problems

Let A = R-{2} and B = R - {1}. If f : A rarr B is a function defined by f(x)= (x-1)/(x-2) then show that f is one-one and onto. Hence, find f^(-1) .

If A = R -{3} and B = R -{1}. Consider the function f:A to B defined by f(x)=(x-2)/(x-3) , for all x in A . Then, show that f is bijective. Find f^(-1)(x) .

If f:RrarrR defined by f(x)=5x-8 for all x inR , then show that f is invertible. Find the corresponding inverse function.

If f is an invertible function, defined as f(x)= (3x-4)/(5) then write f^(-1) (x).

Show that the function f defined by f(x)=|1-x+|x|| , where x is any real number is a continuous function.

SHARAM PUBLICATION-RELATIONS AND FUNCTIONS-EXAMPLE

Let f : W rarr W be defined as f (x) = x -1 if x is odd and f(x) = x +...
Text Solution
|
If f:R to R is defined as f(x)=10x +7. Find the function g:R to R, suc...
Text Solution
|
If f:R to R is the function defined by f(x)=4x^(3) +7, then show that ...
Text Solution
|
If the function f:RrarrR is given by f (x)=(x)^2+3x+1 and g:RrarrR is ...
Text Solution
|
If S is the set of all rational numbers except 1 and * be defined on S...
Text Solution
|
If S is the set of all rational numbers except 1 and * be defined on S...
Text Solution
|
Construct the multiplication table times7 on the set {1, 2, 3, 4, 5, 6...
Text Solution
|
Consider the binary operation **:R xxR to R and o:R xx R to R defined ...
Text Solution
|
Consider the binary operation **on the set {1, 2, 3 , 4, 5} defined by...
Text Solution
|
If ** is a binary operation on set Q of rational numbers such tht a**b...
Text Solution
|
if ** is the binary operation on N given by a**b= L. C. M of a and b. ...
Text Solution
|
if ** is the binary operation on N given by a**b= L. C. M of a and b. ...
Text Solution
|
Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...
Text Solution
|
Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A s...
Text Solution
|
Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...
Text Solution
|
Prove that for any f:X rarr Y , f o idx = f =idY of.
Text Solution
|
Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...
Text Solution
|
Let f:XrarrY. If there exists a map g:YrarrX such that g of=idxand fo ...
Text Solution
|
If ff(x)=cos[pi^2]x+cos[-pi^2]x where [x] stands for the greatest inte...
Text Solution
|
If f:RrarrR,g :RrarrR and h : RrarrR such that f(x)=x^2, g(x)= tan x a...
Text Solution
|