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If f(x)=x+4, g(x)=2x-1 and h(x) =3x then...

If `f(x)=x+4, g(x)=2x-1` and `h(x) =3x` then find `(fog)oh`.

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To solve the problem, we need to find \((f \circ g) \circ h\), which means we will first find \(g \circ h\) and then apply \(f\) to that result. Let's break it down step by step: 1. **Define the Functions**: - \(f(x) = x + 4\) - \(g(x) = 2x - 1\) - \(h(x) = 3x\) 2. **Find \(g(h(x))\)**: - We need to substitute \(h(x)\) into \(g(x)\). - Since \(h(x) = 3x\), we find \(g(h(x)) = g(3x)\). - Now substitute \(3x\) into \(g(x)\): \[ g(3x) = 2(3x) - 1 = 6x - 1 \] 3. **Find \(f(g(h(x)))\)**: - Now we need to substitute \(g(h(x))\) into \(f(x)\). - We have \(g(h(x)) = 6x - 1\), so we find \(f(g(h(x))) = f(6x - 1)\). - Now substitute \(6x - 1\) into \(f(x)\): \[ f(6x - 1) = (6x - 1) + 4 = 6x - 1 + 4 = 6x + 3 \] 4. **Final Result**: - Therefore, \((f \circ g) \circ h = 6x + 3\). ### Summary of Steps: - Step 1: Define the functions. - Step 2: Calculate \(g(h(x))\) by substituting \(h(x)\) into \(g(x)\). - Step 3: Calculate \(f(g(h(x)))\) by substituting the result from Step 2 into \(f(x)\). - Step 4: Write down the final result.
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