Can you solve this one by showing solutions?

1.f(x)+f(g)=2x-5+4x²

Certainly! Let's solve the equation step by step.

Given equation:
\[ f(x) + f(g) = 2x - 5 + 4x^2 \]

### Step 1: Understand the equation
Here, \( f(x) \) represents some function of \( x \), and \( f(g) \) seems to indicate a function of some expression \( g \). However, the equation lacks clarity since \( g \) isn't specified. Assuming \( f(g) \) should be another function of \( x \), like \( f(g(x)) \), we can proceed by solving it as a typical equation involving \( f(x) \).

### Step 2: Assume \( f(x) = ax^2 + bx + c \)
To find the function \( f(x) \), we can assume it to be a quadratic function:
\[ f(x) = ax^2 + bx + c \]

### Step 3: Express \( f(g(x)) \)
Since \( g \) is not specified, if we consider \( f(g(x)) = f(x) \) (just a placeholder for \( f(x) \)), we then have:
\[ f(x) + f(x) = 2f(x) = 2x - 5 + 4x^2 \]

### Step 4: Set up the equation
Using the assumed form of \( f(x) \):
\[ 2(ax^2 + bx + c) = 4x^2 + 2x - 5 \]

### Step 5: Expand and equate coefficients

Explore how to solve equations involving functions and quadratics with our detailed step-by-step guide. This problem covers key algebraic concepts and quadratic equations. Suitable for Grades 10-12.

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