Home
Class 12
MATHS
The functions defined have domain R...

The functions defined have domain R

Text Solution

Verified by Experts

The correct Answer is:
(A) `rarr` (r ); (B) `rarr` (q); (C ) `rarr` (p); (D) `rarr` (s)
`y=7x+1`
`f(x)=7x+1`

Let `x_(1), x_(2) in D_(f)`,
then `f(x_(1))=f(x_(2))`
`implies 7x_(1)+1=7x_(2)+1impliesx_(1)=x_(2)`
f is one-one, `AAx inR`
Now, `y=7x+1impliesx=(y-1)/(7)`
for each `y in R`, we get `x in R`
f is into function
(B) y = cos x
for `x in[0, pi], y in [-1,1]`
`therefore` f is one-one on `[0 pi]`, `AAx inR,yin[-1,1]`
y is not onto R.
(C ) `y = sin x or f(x) = sin x`
for `x in[0, pi], y in[0, 1]`
`f((pi)/(3))=(sqrt(3))/(2)andf((2pi)/(3))=(sqrt(3))/(2)`
`therefore` f is not one-one on `(0, pi)`, `AAx in R and y in [-1, 1]`
`therefore` f is onto [-1, 1].
(D) y = 1 + In x and f(x) = 1 + In x
y is defined for `x in (0, oo)`
Let `x_(1),x_(2)inD`
then `f(x_(1))=f(x_(2))`
`implies 1+Inx_(1)=1+Inx_(2)`
`implies x_(1)=x_(2)`
`therefore` f is one-one, `AAx in(0, oo)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x)= sqrtx and g(x)= x be two functions defined in the domain R^(+) uu {0} , then find the value of (f+g) (x) .

The function f(x) is defined in [0,1] . Find the domain of f(t a nx)dot

Let f: X rarrY be a function. Define a relation R in X given by R = {(a, b): f(a) = f(b)} . Examine whether R is an equivalence relation or not.

Let f : R rarr R be the function defined by f(x) = 2x - 2 , AA x in R . Write f^(-1) .

Prove that the function defined by f(x)= tan x is a continuous function

If the functions f and g defined from the set of real number R to R such that f(x) = e^(x) and g(x) = 3x - 2, then find functions fog and gof. Also, find the domain of the functions (fog)^(-1) and (gof)^(-1) .

If f : R rarr R be the function defined by f(x) = sin (3x +2) AA x in R . Then , f is invertible .

Is the function defined by f(x)= |x|, a continuous function