Question

If the function u=f(x) is continuous at the point $x=a$ and the
function $y=g\left(u\right)$ is continuous at the point $u=f\left(a\right)$, then the
composite function $y=\left(gof\right)\left(x\right)=g\left(f\right(x\left)\right)$is

• A. continuous at the point $x=f\left(a\right)$.
• B. continuous at the point $x=a$.
• C. discontinuous at the point $x=a$.
• D. continuous at the point $x=g\left(a\right)$.

Answer 1

Answer: (B)

continuous at the point $x=a$.

$y=g\left(f\left(x\right)\right)$

Given that $g\left(u\right)$ is continuous

$\Rightarrow f\left(x\right)=u$

$f\left(x\right)$ is continuous at $x=a$

$\Rightarrow g\left(f\left(x\right)\right)$ is continuous at $x=a$