If g:[-2,2] to R where g(x) = x3 + tanx + (x2+1)/p is an odd functio, then the value of - Maths - Relations and Functions

Question

If g:[-2,2] to R where g(x) = x3 + tanx +
(x2+1)/p is an odd functio, then the value of parametric
p is
(a) -5<p<5
(b) p<5
(c) p>5
(d) None

Shruti Tyagi · Accepted Answer

Dear student,

We have,gx=x3+tanx+x2+1pg-x=-x3+tan-x+-x2+1p⇒g-x=-x3-tanx+x2+1pgx+g-x=0 because gx is an odd function
∴x3+tanx+x2+1p-x3-tanx+x2+1p=0⇒2x2+1p=0⇒0≤x2+1p<1    ∵x∈-2,2 ⇒0≤±22+1p<1⇒0≤5p<1⇒p>5hence option c is correct

Regards

If g:[-2,2] to R where g(x) = x3 + tanx + (x2+1)/p is an odd functio, then the value of parametric p is (a) -5<p<5 (b) p<5 (c) p>5 (d) None

If g:[-2,2] to R where g(x) = x³ + tanx + (x²+1)/p is an odd functio, then the value of parametric p is
(a) -5<p<5
(b) p<5
(c) p>5
(d) None