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{:[g(t)=6t-1],[g(◻)=-7]:}

g(t)=6t−1g(□)=−7 \begin{array}{l}g(t)=6 t-1 \\ g(\square)=-7\end{array}

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Domain and range of absolute value functions: equationsright chevron icon

Full solution

Q. g(t)=6t−1g(□)=−7 \begin{array}{l}g(t)=6 t-1 \\ g(\square)=-7\end{array}
  1. Given function: We are given the function g(t)=6t−1g(t) = 6t - 1 and we need to find the value of tt when g(t)=−7g(t) = -7.
  2. Setting up the equation: To find the value of tt, we set the function equal to −7-7: 6t−1=−76t - 1 = -7.
  3. Solving for t: Now we solve for t by adding 11 to both sides of the equation: 6t−1+1=−7+16t - 1 + 1 = -7 + 1.
  4. Isolating tt: This simplifies to 6t=−66t = -6.
  5. Final answer: Next, we divide both sides of the equation by 66 to isolate tt: 6t6=−66\frac{6t}{6} = \frac{-6}{6}.
  6. Final answer: Next, we divide both sides of the equation by 66 to isolate tt: 6t6=−66\frac{6t}{6} = \frac{-6}{6}. This gives us t=−1t = -1.

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