f(x)=(2x-3)

Here are the key properties of f(x) = 2x − 3 (a linear function):

• Domain: all real numbers
• Range: all real numbers
• Slope: 2
• y-intercept: (0, −3)
• x-intercept: x = 3/2 (point (3/2, 0))
• Derivative: f'(x) = 2
• Second derivative: f''(x) = 0
• Inverse function: f^(-1)(x) = (x + 3)/2
• Composition: f(f(x)) = 4x − 9
• Graph: a straight line with slope 2 crossing the y-axis at −3

Some quick tasks you might want:

• Solve f(x) = c: x = (c + 3)/2
• Find the tangent line at any x0: since the slope is constant, the tangent line is the line itself, y = 2x − 3
• If you want a specific problem (e.g., intercepts for a graph, inverse at a value, or a graph sketch), tell me and I’ll work it out.