Relations and Functions Test

Result

Relations and Functions Test - 83

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Choose correct answer (s) from given choice
If f(x) = x + 4, g (x) = 5x and h(x) = 12/x. Find the value of $${ f }^{ -1 }(g(h(6)))$$

A
10

B
14

C
6

D
0
Question 2
1 / -0

If f(x)=x+tanx and g(x) is inverse of f(x) then g'(x) is equal to

A
$$\dfrac { 1 }{ 1+(g(x)-{ x) }^{ 2 } } $$

B
$$\dfrac { 1 }{ 1-(g(x)-{ x) }^{ 2 } } $$

C
$$\dfrac { 1 }{ 1+(g(x)-{ x) }^{ 2 } } $$

D
$$\dfrac { 1 }{ 2-(g(x)-{ x) }^{ 2 } } $$
Question 3
1 / -0

If $$f : N\rightarrow N$$ be defined by $$f(x) = 2x + 3$$ then $$f^{-1} (x) =$$

A
$$2x - 3$$

B
$$\dfrac {x - 3}{2}$$

C
$$\dfrac {x + 3}{2}$$

D
Not defined
Question 4
1 / -0

If f(x) = x + 4, g(x) = 5x and h(x) = 12/x. find the value of $$f^{ -1 }$$ (g(h(6))).

A
10

B
14

C
6

D
0

Solution
Question 5
1 / -0

Let $$f(x)=x+\cos x+2$$ and g(x) be the inverse function of f(x) then $$g^1(3)=$$

A
$$1$$

B
$$2$$

C
$$3$$

D
$$0$$

Solution
Question 6
1 / -0

Number of solution of the equation $$f ( x ) = g ( x )$$ are same as number of point of intersection of the curves $$y = f ( x )$$ and $$y = g ( x )$$ hence answer the following question.
Number of the solution of the equation $$2 ^ { x } = | x - 1 | + | x + 1 |$$ is

A
$$0$$

B
$$1$$

C
$$2$$

D
$$\infty$$

Solution
Question 7
1 / -0

If $$f(x_{1})=f(x_{2})\Rightarrow x_{1}=x_{2}\forall x_{1},x_{2}\epsilon A$$, then what type of a function is $$f:A\rightarrow B?$$

A
One-one

B
Constant

C
Onto

D
Many one

Solution
Question 8
1 / -0

If $$g(x)-x^{2}-x+1 and f(x)=\sqrt{\frac{1}{x}-x}$$, then-

A
Domain of f(g(x)) ids[0,1]

B
Range of f(g(x)) is $$(0,\frac{7}{2\sqrt{3}})$$

C
f (g(x)) is many -one function

D
f(g(x)) is unbounded function
Question 9
1 / -0

$$f: ( 0,\infty )\rightarrow [0,\infty )$$ defined by $$f(x)=x^{2}$$ is

A
one - one but not onto

B
onto but not one - one

C
bijective

D
neither one - one nor onto

Solution
Question 10
1 / -0

If $$f(x)=\frac{1}{x},g(x)=\frac{1}{x^{2}} $$ and h $$(x)= x^{2},$$ then

A
$$fog (x)= x^{2}, x\neq \bar{0}, h(g(x))= \frac{1}{x^{2}}$$

B
$$h(g(x))= \frac{1}{x^{2}}x\neq 0, fog(x)= x^{2}$$

C
$$fog(x)=x^{2},x\neq 0,h(g(x))= (g(x))^{2},x\neq 0$$

D
None of these

Solution