If `f(x)=x^n` and `f'(1)=5` show that `n=5`

Let f : N to N : f(x) =2 x for all x in N Show that f is one -one and into.

If Delta = |(f(x),f(1/x)+f(x)), (1,f(1/x))|=0 where it is given f(x) = a + bx^n and f(2) = 17 and f(5) = K then K-620=

f:[0,5]rarrR,y=f(x) such that f''(x)=f''(5-x)AAx in [0,5] f'(0)=1 and f'(5)=7 , then the value of int_(1)^(4)f'(x)dx is

Let f(x): R^+ to R^+ is an invertible function such that f^(prime)(x)>0a n df"(x)>0AAx in [1,5]dot If f(1)=1 and f(5)=5 and area under the curve y=f(x) on x-axis from x=1tox=5i s8 sq. units, then area bounded by y=f^(-1)(x) on x-axis from x=1tox=5 is

If y=f(x)=(5x+3)/(4x-5) , then show that f(y)=x.

If f(x) = (x^n-a^n)/(x-a) , then f'(a) is a. 1 b. 1/2 c. 0 d. does not exist

Let f: N -> R be a function defined as f(x)=4x^2+12 x+15. Show that f: N -> S, where S is the range of f is invertible. Also find the inverse of f

Let f : N ->R be a function defined as f(x)=4x^2+12 x+15 . Show that f : N-> S , where, S is the range of f, is invertible. Find the inverse of f.

Let f: N -> S be a function defined as f(x)=9x^2+6x-5 . Show that f:N -> S, where S is the range of f , is invertible. Find the inverse of f and hence f^(-1)(43) and f^(-1)(163)

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to