What is the value of $f(0)$ for the function $f(x) = \log_{10} 10 + 9^x + (x - 2)(x - 1)$?

Neetesh Kumar | October 23, 2024

College Algebra Homework Help

CLEPS College Algebra Guide Question 74
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Step-by-step solution:

We need to find ( f(0) ), which means substituting ( x = 0 ) into the function.

Step 1: Evaluate ( \log_{10} 10 )

We know that:

$\log_{10} 10 = 1$

So, the first term is 1.

Step 2: Evaluate ( 9^x ) at ( x = 0 )

When ( x = 0 ), we have:

$9^0 = 1$

Step 3: Evaluate ( (x - 2)(x - 1) ) at ( x = 0 )

Substitute ( x = 0 ) into the expression ( (x - 2)(x - 1) ):

$(0 - 2)(0 - 1) = (-2)(-1) = 2$

Step 4: Add the terms together

Now, add all the evaluated terms:

$f(0) = 1 + 1 + 2 = 4$

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Final Answer:

The value of ( f(0) ) is: $\boxed{4}$

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