plz provide solution of question 122 in detail 122 Let f:R→A=y|0≤y 2 be a function such that - Maths - Relations and Functions

Question

plz provide solution of question 122 in detail

122 Let f : R → A = y | 0 ≤ y < π 2 be a function
such that f(x) = tan–1(x2 + x + k)
where k is a constant
The value of k for which f is an onto function is:
(a) 1
(b) 0
(c) 1 4
(d) none of these

Zuhaib Ul Zamann · Accepted Answer

Dear student,
Range is [0,π/2)So we have tan-1(x2+x+k)∈[0,π/2)x2+x+k∈[0,∞)Hence min(x2+x+k)=0Now we know that min of quadratic ax2+bx+c occurs at x=-b2aHence  -122-12+k=0k=12-14=14Regards

plz provide solution of question 122 in detail 122. Let f : R → A = y | 0 ≤ y < π 2 be a function such that f(x) = tan–1(x2 + x + k) where k is a constant. The value of k for which f is an onto function is: (a) 1 (b) 0 (c) 1 4 (d) none of these

plz provide solution of question 122 in detail

122. Let $f : R \to A = \{y | 0 \leq y < \frac{π}{2}\}$ be a function such that f(x) = tan^–1(x² + x + k) where k is a constant.
The value of k for which f is an onto function is:
(a) 1
(b) 0
(c) $\frac{1}{4}$
(d) none of these