##
**
Question
**

##
Professor Gaekwad develops a machine which can add, subtract, combine and evaluate any two functions. It has an input machine which can accept the functions within its domain. It has an output unit which displays the result and a processor used for calculations. He gives the inputs as
*
f(x)
*
= cos x and
*
g(x)
*
= x
^{
2
}
.

##
**
Question 1
**

##
The domain of f(x) is _______.

(a) [0, 𝜋] (b) [–1, 1]

(c) [(-π)/2,π/2] (d) R

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**
Question 2
**

##
The range of g(x) is _______.

(a) [0, 1] (b) [–1, 1]

(c) R (d) [0, ∞)

##
**
Question 3
**

##
(
*
f + g
*
)(0) = _______.

(a) 0 (b) 1

(c) –1 (d) 2

##
**
Question 4
**

##
*
fog
*
(x) = _______.

(a) cos
^{
2
}
x (b) cos(x
^{
2
}
)

(c) 2cos x (d) cos 2

##
**
Question 5
**

##
gof(x) = is _______.

(a) cos
^{
2
}
x (b) cos(x
^{
2
}
)

(c) 2cos x (d) cos 2