Question

F: x→ 4x+7 then F:x→ −3

It says the answer is 5 but I don't understand

Answer 1

`x=-(5)/(2)`

Explanation:

Given:

`\text{F$:x \rightarrow 4x+7$ then F$:x \rightarrow -3$}`

A function, its domain, and its codomain are given as:

`f:x \rightarrow y`

Therefore:

`\text{F$:x \rightarrow 4x+7$\; is the same as \;$f(x)=4x+7$}`

`\text{F$:x \rightarrow -3$ \; is the same as \; $f(x)=-3$}`

To find the value of x that makes both functions true, equate the functions and solve for x:

`\begin{aligned}f(x)&=-3\\\implies 4x+7&=-3\\4x+7-7&=-3-7\\4x&=-10\\(4x)/(4)&=(-10)/(4)\\x&=-(5)/(2)\end{aligned}`

Check by inputting the found value of x into the first function:

`\begin{aligned}x=-(5)/(2) \implies f\left(-(5)/(2)\right)&=4\left(-(5)/(2)\right)+7\\&=-10+7\\&=-3\end{aligned}`