Learn Transformations of Functions with Plainmath's In-Depth Explanations and Real-World Examples

g(x)
${\displaystyle =\frac{2x^2-3x-20}{x-4},\text{if}x\ne 4}$
and
$=kx-15$, if $x=4$
Evaluate the constant k that makes the function continuous.

${\displaystyle f:R\to R}$
$f(x)=7x-3$
Prove that f is onto.

$n=3$, 4 and 2i are zeros.
$f(-1)=75$
Find an nth-degree polynomial function with real coefficients

Given an indicated variable:
$S=180n-360$
Solve it for n

${\displaystyle f:R\to R}$
$f(x)=8x-2$
$f(a)=f(b)$
${\displaystyle a,b\in R}$
Prove that f is one-to-one.

Show that $f(x)=x-6$ and $g(x)=x+6$ are inverses of each other.

Transform the equation $r=12$ from polar to rectangular form.

Find $f(x)$ and $g(x)$, if ${\displaystyle H\left(x\right)=|8-x^6|}$

Given:
${\displaystyle \frac{m}{8}=\frac{15}{24}}$
Is ${\displaystyle 8\times m=25\times 15}$ true or false? Correct if false. Find m.

${\displaystyle f\left(x\right)=9,\text{if}x\le -4,\text{and}f\left(x\right)=ax+b,\text{if}-4<x<5,\text{and}f\left(x\right)=-9,\text{if}x\ge 5,}$
Find the constants, if the function is continuous on the entire line.