Functions - composition and inverse

1.      If the mapping f: R to R be given by f(x) = 4x-1 and the mapping g: R to R be given by g(x) = x³ + 2 the find gof and fog

2.      If f and g are two mappings from R to R given by f(x) = x² + 3x+1 and g(x)=2x-3 find fog and gof

3.      Let f: R to R be given by f(x) = x³ -2 find fof

4.      Let f: R to R, g: R to R and h: R to R be such that f(x) = x² -2 , g(x) = x+4 and h(x) = x+4. Find hof, gof, goh. Also find the inverse of f, g and h

5.      Let f : R to R be f(x) = (2x-1)/3. Find f^-1

6.      f, g ,h are functions on X = {1,2,3} as

f = {(1,2) (2,3) (3,1)}

g={(1,2) (2,1) (3,1)}

h={(1,1)(2,2)(3,1)}

compute fog, gof, fogoh and fohog

7.      let f: Z to Z where f(x) = x+4. Is f invertible?

8.      Let f: N to N where f(x) = x+3 . Is f invertible?

9.      Let f: Z to Z where f(x) = x²-1. Is f invertible?

10.  Le the function f be defined by f(x) = (2x+1)/(1-3x) then find f^-1

11.  If f(x)= [4-(x-7)³]^1/5 is a real function then find f^-1

12.  f:R to R is a function defined by f(x)=10x-7. If g=f^-1. Find f^-1

13.  If f(x)= (1+x)/(1-x) then show that f^-1(y) = (y-1)/(y+1)

14.  Let f:N to Y  where Y= {y in N: y= 4x+3} be a function defined as f(x)=4x+3. Show that f is invertible.

15.  Let g(x)= (x+2)/(x-1). Find g^-1