Functions Test 59

Result

Functions Test 59

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Weekly Quiz Competition

Question 1
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 2
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 3
1 / -0

Let D = [-1, 1] is the domain of the following functions, state which of them are injective

A
$$f\left( x \right) = \dfrac{{{{\tan }^{ - 1}}1}}{x},x \ne 0$$

B
$$g(x)={ x }^{ 2 }$$

C
$$h(x)=sin2x$$

D
$$k(x)=sin(\pi x/2)$$

Solution
Question 4
1 / -0

If =$$f=\left\{ (-2,4),(0,6),(2,8) \right\} $$ and
$$g=\left\{ (-2,-1),(0,3),(2,5) \right\} $$, then
$$\left( \frac { 2f }{ 3g } +\frac { 3g }{ 2f } \right) (0)=\quad $$

A
1/12

B
25/12

C
5/12

D
13/12

Solution
Question 5
1 / -0

Domain of $$\frac{3^{x}}{x+1}$$ is

A
R

B
R-{-1}

C
$$(1,\infty )$$

D
$$(-\infty ,1)$$
Question 6
1 / -0

The domain of $$cos h^{-1}5x$$ is

A
R

B
$$[0,\infty )$$

C
$$(\frac{1}{5},\infty )$$

D
$$[\frac{1}{5},\infty )$$

Solution
Question 7
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
Question 8
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 $$x ^ { 2 } = | x - 2 | + | x + 2 | - 1$$ is

A
$$0$$

B
$$3$$

C
$$2$$

D
$$4$$

Solution
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

The domain of the function $$f ( x ) = \sin ^ { - 1 } \left( \left( 1 + e ^ { x } \right) ^ { - 1 } \right)$$ is

A
$$R$$

B
$$[ - 1,0 ]$$

C
$$[ 0,1 ]$$

D
$$[ - 1,1 ]$$

Solution