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###### Vaishnavi Mishra posted an Question
December 15, 2021 • 12:45 pm 30 points
• IIT JAM
• Mathematics (MA)

## 1) the real continuous functions f and g defined on r commute that is f(gx)) = g(f)) for x e r and if the equation f2(x) = g2(x) has a solution then a) f(x) = g

1) The real continuous functions f and g defined on R commute that is f(gx)) = g(f)) for x E R and if the equation f2(x) = g2(x) has a solution then a) f(x) = g(x) also has a solution [b) f(x) = g(x) also has a solution (c) f(x) =g(x) may or may not have a solution (d) None of these

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• ##### Pranshu

check attachment what you are satisfied with the solution ?

• ##### Vaishnavi mishra

×2= ×4 kaise equal hoga plz explain

x=x⁴

sir eske koi theorem hai ya kuchh proof hai mujhe exact nhi samjh aa rha hai ki solution kb solution exit karega f(×) g(×) ke equal nhi hai

• ##### Pranshu

Navdeep sir can my answer is also right ?

• ##### Navdeep goyal 1

f(x)=x, g(x) =x² fog(x)= x² and gof(x) =x² fog=gof f²(x)=x g²(x)=x⁴ x²=x⁴ has a solution f(x)=g(x)=>x=x² has also solution