Suppose that `f(x)=5x−3 and g(x)=−2x+4`
(a) Solve `f(x)=0`
(b) Solve `f(x) gt 0`
(c) Solve `f(x)=g(x)`
(d) Solve `f(x) le g(x)`
(e) Graph `y=f(x) and y=g(x)` and find the point that represents the solution to the equation `f(x)=g(x)`

Suppose that f(0)=0 and f'(0)=2, and g(x)=f(-x+f(f(x))). The value of g'(0) is equal to -

If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x)) is equivalent to (A) f(a) = g(c ) (B) f(b) = g(b) (C) f(d) = g(b) (D) f(c ) = g(a)

Let f(x) and g(x) be two real valued functions then |f(x) - g(x)| le |f(x)| + |g(x)| Let f(x) = x-3 and g(x) = 4-x, then The number of solution(s) of the above inequality when x ge 4 is

Let f(x) and g(x) be two real valued functions then |f(x) - g(x)| le |f(x)| + |g(x)| Let f(x) = x-3 and g(x) = 4-x, then The number of solution(s) of the above inequality for x lt 3 is

f(x)=(x-k)/(5) and g(x)=5x+7 . If f(g(x))=g(f(x)) , what is the value of k?

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

If f(x)=|x-2|" and "g(x)=f(f(x)), then for 2ltxlt4,g'(x) equals

If f(x+2)=3x+11 and g(f(x))=2x, find the value of g(5).

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}