Recent questions in Transformations of functions
Transformations of functions

### Express the area of a rectangle bounded by the x- and y-axes and the graph of $$\displaystyle{y}=−\frac{{1}}{{2}}{x}+{4}$$.

Transformations of functions

### Show that f is inverse of g and vice-versa, if $$f(x)=x-6$$ and $$g(x)=x+6$$

Transformations of functions

### Convert the function $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{4}{x}+{5}$$ into vertex form.

Transformations of functions

### Is $$\displaystyle{f{{\left({s}\right)}}}={x}^{{3}}$$ a bijection from $$\displaystyle\mathbb{R}$$ to $$\displaystyle\mathbb{R}$$?

Transformations of functions

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

Transformations of functions

### A(3,5), B(0,4), C(-2,-2) k = 2 Find the coordinates of the vertices after dialation with given k

Transformations of functions

### x=-8, when $$\displaystyle{y}=-\frac{{1}}{{4}}$$ in an inverse variation. Find y, when x=4

Transformations of functions

### $$\displaystyle{{f}^{{-{1}}}{\left({4}\right)}}=-{7}$$ $$\displaystyle{f{{\left(-{7}\right)}}}=?$$

Transformations of functions

### Rectangular equation is xy=5. Transform it into polar equation.

Transformations of functions

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

Transformations of functions

### Find domain of fog, if 1. $$\displaystyle{f{{\left({x}\right)}}}={x}+{5}.{g{{\left({x}\right)}}}=\frac{{7}}{{{x}+{7}}}$$ 2. $$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{x}}.{g{{\left({x}\right)}}}={6}{x}+{18}$$

Transformations of functions

### The line $$\displaystyle{y}=\frac{{4}}{{5}}{x}+{2}$$ passes through (1,2) Express a line parallel to it with an equation.

Transformations of functions

### Given: $$\displaystyle{E}{\left({t}\right)}={L}{\left({t}\right)}+{C}{\left({t}\right)}$$ $$\displaystyle{E}{\left({t}\right)}={k}{{\sin}^{{2}}{\left({2}\pi{F}{t}\right)}}+{k}{{\cos}^{{2}}{\left({2}\pi{F}{t}\right)}}$$ Prove that E is a constant function, if k is constant.

Transformations of functions

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

Transformations of functions

### What is the percent rate of the following function: $$\displaystyle{y}={2}{\left({0.69}\right)}^{{t}}$$

Transformations of functions

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

Transformations of functions

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

Transformations of functions

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

Transformations of functions