Use the function f(x) = 2x3 - 3x2 + 7 to find f (−1), f (1) and f (2).

The relationship between an independent variable and a dependent variable is defined by an expression, rule of law called a function. A function is often denoted as f(x).

Answer: The values of f (-1) is 2, f (1) is 6 and f (2) is 11 for the function f (x) = 2x3 - 3x2 + 7

Let's find the value of f (−1), f(1) and f(2)

Explanation:

Given the function f(x) = 2x3 - 3x2 + 7

To find the values of f(-1), we will substitute x = -1 in f(x)

⇒ f (-1) = 2 (-1)3 - 3 (-1)2 + 7

= -2 - 3 + 7

= -5 + 7 = 2

To find the values of  f(1), we will substitute x = 1 in f(x)

⇒ f(1) = 2 (1)3 - 3 (1)2 + 7

= 2 - 3 + 7

= -1 + 7 = 6

To find the values of  f(2), we will substitute x = 2 in f(x)

⇒ f (2) = 2 (2)3 - 3 (2)2 + 7

= 2 × 8 - 3 × 4 + 7

= 16 - 12 + 7

= 4 + 7 = 11

Thus, the values of f(-1) is 2, f(1) is 6 and f(2) is 11 for the function f(x) = 2x3 - 3x2 + 7

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