Question

Find the x-values at which f is not continuous.f(x) = tan(πx/2)

Answer 1

Answer:

$x\neq 1+2n,n\in\mathbb{Z}$

Step-by-step explanation:

Remember that for the tangent parent function, it has infinite discontinuities (vertical asymptotes) on:

$f(x)=\tan(x), \\\text{Where }x\neq\frac{\pi}{2}+n\pi, n\in\mathbb{Z}$

Here, we have:

$f(x)=\tan(\frac{\pi x}{2})$

So, we can set the expression inside the tangent to equal our parent domain restriction. This yields:

$\frac{\pi x}{2}\neq\frac{\pi}{2}+n\pi$

Solve for x. Multiply both sides by 2:

$\pi x\neq \pi+2n\pi$

Divide both sides by π:

$x\neq 1+2n, n\in\mathbb{Z}$

Therefore, for the function $f(x)=\tan(\frac{\pi x}{2})$, it is not continuous for all Xs $1+2n$ where $n\in\mathbb{Z}$