Question

if f:r is rn g:r is defined by f(x) =3x+1 g(x)÷x^2+1 then find fog(2) ,gof(2a-3)​

Answer 1

Answer:              f:R→R

f(x)=x  

2

+2

g:R→R

g(x)=  

x−1

x

​  

 

fog(x)=f(g(x))

=f(  

x−1

x

​  

)

=(  

x−1

x

​  

)  

2

+2

=  

x  

2

−2x+1

x  

2

 

​  

+2

=  

x  

2

−2x+1

x  

2

+2(x  

2

−2x+1)

​  

 

=  

x  

2

−2x+1

x  

2

+2x  

2

−4x+2

​  

 

=  

x  

2

−2x+1

3x  

2

−4x+2

​  

 

fog(2)=  

2  

2

−2×2+1

3×2  

2

−4×2+2

​  

 

=  

4−4+1

3×4−8+2

​  

 

=  

1

12−6

​  

 

=6

gof(x)=g(f(x))

=g(x  

2

+2)

=  

x  

2

+2−1

x  

2

+2

​  

 

=  

x  

2

+1

x  

2

+2

​  

 

gof(−3)=  

(−3)  

2

+1

(−3)  

2

+2

​  

 

=  

9+1

9+2

​  

 

=  

10

11

​

Step-by-step explanation: