Find the following for the function fx xx21 a f0 f5 fminus5

Find the following for the function f(x) =x/x^2+1

(a) f(0)

f(5)

f(minus5)

f(minusx)

minusf(x)

f(xplus+1)

f(4x)

f(xplus+h)

(a)

f(0)equals=nothing

(Simplify your answer. Type an integer or a simplified fraction.)

(b)

f(5)equals=nothing

(Simplify your answer. Type an integer or a simplified fraction.)

(c)

f(minus5)equals=nothing

(Simplify your answer. Type an integer or a simplified fraction.)

(d)

f(minusx)equals=nothing

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

(e)

minusf(x)equals=nothing

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

(f)

f(xplus+1)equals=nothing

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

(g)

f(4x)equals=nothing

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

(h)

f left parenthesis x plus h right parenthesisf(x+h)equals=nothing

(a) f(0)	(b) f(5)	(c) f(minus5)	(d) f(minusx)
(e) minusf(x)	(f) f(xplus+1)	(g) f(4x)	(h) f(xplus+h)

Solution

given f(x) =x/(x^2+1)

a)f(0)= 0/(0^2 +1)

f(0)=0

b) f(5) =5/(5^2+1)

f(5) =5/(25+1)

f(5)=5/26

c)

f(-5) =-5/((-5)^2+1)

f(-5) =-5/(25+1)

f(-5)=-5/26

d)f(-x) =(-x)/((-x)^2+1)

f(-x) =-x/(x^2+1)

e)f(x)=-x/(x^2+1)

f) f(x+1) =(x+1)/((x+1)^2+1)

f(x+1) =(x+1)/(x^2+2x+1+1)

f(x+1) =(x+1)/(x^2+2x+2)

g)f(4x)=4x/((4x)^2+1)

f(4x)=4x/(16x^2+1)

h)f(x+h) =(x+h)/((x+h)^2+1)

f(x+h) =(x+h)/(x^2 +2xh+h^2+1)