`f(x)=|x-2|+|x-3|,p r o v e t h a tint_2^4f(x)dx=3`

Let f(x) be a continuous function AAx in R , except at x=0, such that int_x^a(f(t))/t dt ,p rov et h a tint_0^af(x)dx=int_0^ag(x)dx

If f(x)={e^(cosxsinx ,for|x|lt=2)2,ot h e r w i s e ,t h e nint_(-2)^3f(x)dx= 0 (b) 1 (c) 2 (d) 3

If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

If a function f (x) is given as f (x) = x^(2) -3x +2 for all x in R, then f (a +h)=

If a function f (x) is given as f (x) = x^(2) -3x +2 for all x in R, then f (a +h)=

If f: R to R is defined by f(x) = 2x+|x| , then show that f(3x) -f(-x) -4x=2f(x) .

If f(x)=2x+3 , g(x)=1-2x and h(x)=3x. Prove that f o(g o h) = (f o g ) o h

If f(x)=2x+3, g(x) = 1-2x and h(x)=3x . Prove that f o (g o h) = (f o g) o h

Let f_1:R→R,f_2:[0,∞)→R, f_3:R→R and f_4:R→[0,∞) be defined by f_1(x)={ ∣x∣ if x<0 ; e^x if x≥0 ; f_2(x)=x^2 ; f_3(x)={ sin x if x<0 ; x if x≥0 ; f_4(x)={ f_2(f_1(x)) if x<0 f_2(f_1(x)) if x≥0 ​then f_4 is