Which function is the inverse of f(x) =2x +3

Mathematics

2 answers:

frosja888 [35]2 years ago

5 0

Answer:

-1

f (x) = x/2 - 3/2

Step-by-step explanation:

I choose to address this question by actually finding the inverse of f(x) = 2x + 3.

1) replace f(x) with y: y = 2x + 3

2) interchange x and y: x = 2y + 3

3) solve this result for y: 2y = x - 3 , or y = (x - 3)/2. This is the same as the second answer choice. Label this result as

-1

f (x) = x/2 - 3/2

lesya692 [45]2 years ago

4 0

F(x)=
$f(x) = 2x + 3$
$let y = 2x + 3$
make y subject of the formula
$x = \frac{y - 3}{2}$
replace y with x above
$f ^{ - 1 } = \frac{x - 3}{2}$

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What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)

lutik1710 [3]

so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).

$\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}$

so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?

$\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill$