Video Transcript
Consider the function 𝑓 of 𝑥 equals negative four multiplied by 𝑔 of 𝑥, where 𝑔 of 𝑥 is equal to 𝑥 plus six. What is the value of 𝑓 of two?
We are told in the question that 𝑔 of 𝑥 is equal to 𝑥 plus six. The function 𝑓 of 𝑥 is equal to negative four multiplied by the function 𝑔 of 𝑥. This means that 𝑓 of 𝑥 is equal to negative four multiplied by 𝑥 plus six. We can simplify this function by distributing the parenthesis, multiplying negative four by 𝑥 and negative four by six. Negative four multiplied by 𝑥 is equal to negative four 𝑥. And negative four multiplied by positive six is equal to negative 24. Multiplying a negative number by a positive number gives us a negative answer. The function 𝑓 of 𝑥 is equal to negative four 𝑥 minus 24.
We are asked to calculate the value of 𝑓 of two. This means that we need to substitute 𝑥 equals two into the function 𝑓 of 𝑥. 𝑓 of two is equal to negative four multiplied by two minus 24. Negative four multiplied by two is equal to negative eight. We need to subtract 24 from negative eight. This gives us an answer of negative 32. When we are subtracting from a negative number, we go further down our number line. This means that the answer becomes more negative. If 𝑔 of 𝑥 is equal to 𝑥 plus six, and 𝑓 of 𝑥 is equal to negative four multiplied by 𝑔 of 𝑥, then 𝑓 of two is equal to negative 32.
