If : $$ f(X)=2 X+b $$ and $$ g(X)=\mathrm{b} $$ where $$ f, g $$ from the polynomial functions and $$ f(1)+g(4)=12 $$ Find the value of : $$ f(4)+g(-1) $$

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UpStudy AI · Accepted Answer

To solve the problem, we start with the given functions:

$$
f(X) = 2X + b
$$
$$
g(X) = b
$$

We also know that:

$$
f(1) + g(4) = 12
$$

First, we calculate $$ f(1) $$ and $$ g(4) $$:

$$
f(1) = 2(1) + b = 2 + b
$$
$$
g(4) = b
$$

Now, substituting these into the equation:

$$
f(1) + g(4) = (2 + b) + b = 2 + 2b
$$

Setting this equal to 12 gives us:

$$
2 + 2b = 12
$$

Subtracting 2 from both sides:

$$
2b = 10
$$

Dividing by 2:

$$
b = 5
$$

Now that we have $$ b $$, we can find $$ f(4) $$ and $$ g(-1) $$:

Calculating $$ f(4) $$:

$$
f(4) = 2(4) + b = 8 + 5 = 13
$$

Calculating $$ g(-1) $$:

$$
g(-1) = b = 5
$$

Now we can find $$ f(4) + g(-1) $$:

$$
f(4) + g(-1) = 13 + 5 = 18
$$

Thus, the final answer is:

$$
\boxed{18}
$$
The value of $$ f(4) + g(-1) $$ is 18.

If : \( f(X)=2 X+b \) and \( g(X)=\mathrm{b} \) where \( f, g \) from the polynomial functions and \( f(1)+g(4)=12 \) Find the value of : \( f(4)+g(-1) \)

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