Solve the Inequalities

Question

a) If f(x) is a decreasing function (that is, the graph of f always move down as you move from left to right), with f(5)=2, solve the inequality for f(x)>2

b) If f(x) is an increasing function with f(5)=2, solve the inequality f(x)>2

Please help knowing the information! It would truly be appreciated.

Answer 1

a) Since f is decreasing we have that the inequality f(x)>2=f(5) holds true if and only if x<5.

b) Since f is increasing we have that the inequality f(x)>2=f(5) holds true if and only if x>5.