Question -
Answer -
(i) f(x)= 
We know that 
for every x ∈ R. Therefore, f(x) = 
for every x ∈ R.The minimum value of f is attainedwhen 
.
∴Minimum value of f = f(−2)
Hence, function f does nothave a maximum value.
(ii) g(x) =
We know that 
for every x ∈ R. Therefore, g(x) = 
for every x ∈ R. The maximum value of g is attainedwhen
∴Maximum value of g = g(−1)= 
Hence, function g does nothave a minimum value.
(iii) h(x) = sin2x +5
We know that − 1 ≤ sin 2x ≤ 1.
⇒ − 1 + 5 ≤ sin 2x + 5 ≤ 1 + 5
⇒ 4 ≤ sin 2x + 5 ≤ 6
Hence, the maximum and minimum valuesof h are 6 and 4 respectively.
(iv) f(x) =
We know that −1 ≤ sin 4x ≤ 1.
⇒ 2 ≤ sin 4x + 3 ≤ 4
⇒ 2 ≤≤ 4 Hence, the maximum and minimum valuesof f are 4 and 2 respectively.
(v) h(x) = x +1, x ∈ (−1, 1)
Here, if a point x0 isclosest to −1, then we find 
for all x0 ∈ (−1, 1). Also, if x1 isclosest to 1, then 
for all x1 ∈ (−1, 1). Hence, function h(x) hasneither maximum nor minimum value in (−1, 1).