Math Problem Statement

Given f(x) = (3x^2 - 2x + 1) / x^2, find the following: (a) f(1) (b) f(-1) (c) f(2) (d) lim x -> infinity f(x) (e) lim x -> 0+ f(x)

Solution

The image you uploaded contains a question that involves evaluating a given function at various points. The function appears to be of the form:

f(x)=3x22x+1x2f(x) = \frac{3x^2 - 2x + 1}{x^2}

The task involves finding specific function values, as indicated in the following subparts:

(a) f(1)f(1)
(b) f(1)f(-1)
(c) f(2)f(2)
(d) limxf(x)\lim_{x \to \infty} f(x)
(e) limx0+f(x)\lim_{x \to 0^+} f(x)

It seems like you got some answers right and others incorrect. I’ll go through each part step-by-step to help you with the evaluation.

(a) f(1)f(1)

Substitute x=1x = 1 into the function:

f(1)=3(1)22(1)+1(1)2=32+11=21=2f(1) = \frac{3(1)^2 - 2(1) + 1}{(1)^2} = \frac{3 - 2 + 1}{1} = \frac{2}{1} = 2

This matches the correct answer indicated in your image.

(b) f(1)f(-1)

Substitute x=1x = -1 into the function:

f(1)=3(1)22(1)+1(1)2=3(1)+2+11=3+2+11=6f(-1) = \frac{3(-1)^2 - 2(-1) + 1}{(-1)^2} = \frac{3(1) + 2 + 1}{1} = \frac{3 + 2 + 1}{1} = 6

(c) f(2)f(2)

Substitute x=2x = 2 into the function:

[ f(2) =

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Math Problem Analysis

Mathematical Concepts

Rational Functions
Limits
Evaluating Functions

Formulas

f(x) = (3x^2 - 2x + 1) / x^2
Limit formulas for rational functions

Theorems

Limit Theorem
Continuity at a Point

Suitable Grade Level

Grades 10-12